Related papers: Second-order self-consistent field algorithms: fro…
The implementation of an efficient self-consistent field (SCF) method including both scalar relativistic effects and spin-orbit interaction in density functional theory (DFT) is presented. We make use of Gaussian-type orbitals (GTOs) and…
In this contribution, we present the implementation of a second-order CASSCF algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called Norm-Extended Optimization, guarantees…
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in…
In this work, we develop a new orbital optimization approach, perturbative Super-CI (Super-CIPT), for the two-component complete active space self-consistent field (2C-CASSCF) method. By variationally optimizing spinor orbitals and…
We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection to the minimization problem of the sum of a convex lower semi-continuous function $f$ and a…
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the p-Laplacian, an optimal design problem in topology…
High-dimensional and incomplete (HDI) data, characterized by massive node interactions, have become ubiquitous across various real-world applications. Second-order latent factor models have shown promising performance in modeling this type…
We construct new static, spherically symmetric non-extremal black hole solutions of four-dimensional ${\cal N}=2$ supergravity, using a systematic technique based on dimensional reduction over time (the c-map) and the real formulation of…
Over the past few decades, kernel-based approximation methods had achieved astonishing success in solving different problems in the field of science and engineering. However, when employing the direct or standard method of performing…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…
This paper investigates the time fractional sine-Gordon equation whose solution exhibits a weak singularity of type t^{\alpha}. By means of the Alikhanov formula we derive a fully discrete, linearized scheme. Using the more general…
We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Pad\'e approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order…
An approximation to General Relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved…
Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts approximate…
We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
In the past decade, natural orbital functional (NOF) approximations have emerged as prominent tools for characterizing electron correlation. Despite their effectiveness, these approaches, which rely on natural orbitals and their associated…
Second-order optimizers are thought to hold the potential to speed up neural network training, but due to the enormous size of the curvature matrix, they typically require approximations to be computationally tractable. The most successful…
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…